yx²+3yx+4y=x²-3x+4
(y-1)x²+(3y+3)x+(4y-4)=0
x是实数则方程有解
所以判别式大于等于0
9y²+18y+9-16y²+32y-16>=0
7y²-50y+7<=0
(7y-1)(y-7)=0
1/7<=y<=7
所以最大值=7,最小值=1/7